Sorting AlgorithmsInsertion and Radix Sort

Insertion Sort

One by one, each as yet unsorted array element is inserted into its proper place with respect to the already sorted elements.

On each pass, this causes the number of already sorted elements to increase by one.

values [ 0 ]

[ 1 ]

[ 2 ]

[ 3 ]

[ 4 ]

36

10

24

6

12

Insertion Sort

Works like someone who “inserts” one more card at a time into a hand of cards that are already sorted.

To insert 12, we need to make room for it by moving first 36 and then 24.

6 10 24

12

36

Insertion Sort

6 10 24

Works like someone who “inserts” one more card at a time into a hand of cards that are already sorted.

To insert 12, we need to make room for it by moving first 36 and then 24.

36

12

Insertion Sort

Works like someone who “inserts” one more card at a time into a hand of cards that are already sorted.

To insert 12, we need to make room for it by moving first 36 and then 24.

6 10 24 36

12

Insertion Sort

Works like someone who “inserts” one more card at a time into a hand of cards that are already sorted.

To insert 12, we need to make room for it by moving first 36 and then 24.

6 10 12 24 36

A Snapshot of the Insertion Sort Algorithm

Insertion Sort

Code for Insertion Sort

void InsertionSort(int values[ ],int numValues)

// Post: Sorts array values[0 . . numValues-1] into // ascending order by key{ for (int curSort=0;curSort<numValues;curSort++) InsertItem ( values , 0 , curSort ) ;}

Insertion Sort code (contd.)

void InsertItem (int values[ ], int start, int end )

{ // Post:Post: inserts values[end] at the correct position // into the sorted array values[start..end-1]

bool finished = false ;int current = end ;bool moreToSearch = (current != start);

while (moreToSearch && !finished ) { if (values[current] < values[current - 1]){

Swap(values[current], values[current - 1);current--;moreToSearch = ( current != start );

} else

finished = true ;}

}

Radix Sort

Radix Sort – Pass One

Radix Sort – End Pass One

Radix Sort – Pass Two

Radix Sort – End Pass Two

Radix Sort – Pass Three

Radix Sort – End Pass Three

Radix Sort

Radix Sort

• Cost:– Each pass: n moves to form groups– Each pass: n moves to combine them

into one group– Number of passes: d– 2*d*n moves, 0 comparison– However, demands substantial

memory • not a comparison sort

Sorting Algorithms and Average Case Number of

Comparisons

Simple Sorts– Selection Sort– Bubble Sort– Insertion Sort

More Complex Sorts– Quick Sort– Merge Sort– Heap Sort

O(N2)

O(N*log N)

• Radix Sort O(dn) where d=max# of digits in any input number

Binary Search

• Given an array A[1..n] and x, determine whether x ε A[1..n]

• Compare with the middle of the array

• Recursively search depending on the result of the comparison